where Mag(x;y) = 1/| det[Jacη](x)| is the magnification of the lensed image x of y. Suppose that the light source at y moves along a path y(t). Then the shifted center-of-light curve relative to the source’s trajectory is defined by Xcl(t) = xcl(y(t)) − y(t). It is an important fact that locally stable k-plane lensing maps η are generic and each is differentiably equivalent about every critical...

We observe the weak S0 → S2 transitions of the T-shaped benzene dimers (Bz)2 and (Bz-d6)2 about 250 cm(-1) and 220 cm(-1) above their respective S0 → S1 electronic origins using two-color resonant two-photon ionization spectroscopy. Spin-component scaled (SCS) second-order approximate coupled-cluster (CC2) calculations predict that for the tipped T-shaped geometry, the S0 → S2 electronic oscill...

A double-loop digraph G=G(N ; s1; s2), with gcd(N; s1; s2)=1, has the set of vertices V =ZN and the adjacencies are given by u → u + si (mod N ) i = 1; 2. The diameter of G, denoted by D(N ; s1; s2), is known to be lower bounded by lb(N ) with D(N ) = min 16s1¡s2¡N; gcd(N;s1 ; s2)=1 D(N ; s1; s2)¿ ⌈√ 3N ⌉ − 2 = lb(N ): This lower bound is known to be sharp. For a 0xed N ∈N, some algorithms to 0...

Let S1 and S2 be Γ-semigroups. In this note, we determine when S1 and S2 are isomorphic if the power semigroup of S1 and the power semigroup of S2 are o-isomorphic.

A bisection of a graph G is a bipartition S1, S2 of V (G) such that −1 ≤ |S1|− |S2| ≤ 1. It is NP-hard to find a bisection S1, S2 of a graph G maximizing e(S1, S2) (respectively, minimizing max{e(S1), e(S2)}), where e(S1, S2) denotes the number of edges of G between S1 and S2, and e(Si) denotes the number of edges of G with both ends in Si. There has been algorithmic work on bisections, but ver...

ABSTRACT Lettuce is a leafy vegetable sensitive to salinity, and under saline stress conditions it presents nutritional imbalance, mainly in calcium absorption. Thus, the objective was evaluate effect of enriching nutrient solution with nitrate solutions prepared water lettuce crop. A completely randomized design used, five treatments four replicates. The were represented by [S1 - standard (SNP...